Consider the connectivity matrix for multilayer feed-forward neural network.

(a) Draw the neural network structure with 2 inputs and 1 output.

(b) Run your network, with your initial weights as all 1s, for the input vector X = {1, -2}

(c) Apply back-propagation algorithm for one iteration and find the next weight matrix using the input X in part (b) with the desired output as 2 (without activation).

Assumptions and Useful Formula:

Activation function = f(z) = 1 / 1+e-z

Derivative of activationfunction = f(z) = z(1-z)

Delta calculations (backward pass): j = (Oj dj) . f(Oj) -- for output neurons

j = fj (Oj) . all i out of j i. wij -- for non-output neurons